Answer:
A.Multiplication Property of EqualityStep-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x+2y=14\\-x+y=5&\text{\underline{multiply both sides by 2}}\end{array}\right\\\\\boxed{\underline{+\left\{\begin{array}{ccc}2x+2y=14\\-2x+2y=10\end{array}\right}}\qquad\text{add both sides of the equations}\\.\qquad\qquad4y=24\qquad\text{divide both sides by 4}\\.\qquad\qquad y=6\\\\\text{put the value of y to the second equation:}\\\\-x+6=5\qquad\text{subtract 6 from both sides}\\-x=-1\qquad\text{change the signs}\\x=1[/tex]
Answer: Its Multiplication property of Equality
Step-by-step explanation: Just did the test
Given f(x) = V6x and g(x) =
-6
Which value is in the domain of fºg?
Click on the correct answer.
Answer:
8 is the only one that will work
Step-by-step explanation:
(f o g)(x)=f(g(x)).
So this means the x will first be plug into g.
So let's check your choices.
g(6)=1/(6-6)=1/0 so 6 is not in the domain of g which means it isn't in the domain of (f o g).
g(8)=1/(8-6)=1/2 so this is a number so 8 is in the domain of g,
Let's check if 1/2 is in the domain of f.
f(1/2)=sqrt(6*1/2)=sqrt(3) so this is a number so since 1/2 is in the domain of f then 8 is in the domain of (f o g).
g(4)=1/(4-6)=1/(-2)=-1/2 so 4 is in the domain of g,
f(-1/2)=sqrt(6*-1/2)=sqrt(-3) so this is a problem because you can't square root negative numbers so -1/2 isn't in the domain of f, and therefore 4 isn't in the domain of (f o g).
g(2)=1/(2-6)=1/-4=-1/4 so 2 is in the domain of g.
f(-1/4)=sqrt(6*-1/4)=sqrt(-3/2) so again this is a problem because we can't square root negative numbers so -1/4 isn't in the domain of f, and therefore 2 isn't in the domain of (f o g).
Cos y/ 1-sin y= 1+sin y/cos y. Verify the identity. Show All Steps!
Answer:
When proving identities, the answer is in the explanation.
Step-by-step explanation:
[tex]\frac{\cos(y)}{1-\sin(y)}[/tex]
I have two terms in this denominator here.
I also know that [tex]1-\sin^2(\theta)=\cos^2(theta)[/tex] by Pythagorean Identity.
So I don't know how comfortable you are with multiplying this denominator's conjugate on top and bottom here but that is exactly what I would do here. There will be other problems will you have to do this.
[tex]\frac{\cos(y)}{1-\sin(y)} \cdot \frac{1+\sin(y)}{1+\sin(y)}[/tex]
Big note here: When multiplying conjugates all you have to do is multiply fist and last. You do not need to do the whole foil. That is when you are multiplying something like [tex](a-b)(a+b)[/tex], the result is just [tex]a^2-b^2[/tex].
Let's do that here with our problem in the denominator.
[tex]\frac{\cos(y)}{1-\sin(y)} \cdot \frac{1+\sin(y)}{1+\sin(y)}[/tex]
[tex]\frac{\cos(y)(1+\sin(y))}{(1-\sin(y))(1+\sin(y)}[/tex]
[tex]\frac{\cos(y)(1+\sin(y))}{1^2-\sin^2(y)}[/tex]
[tex]\frac{\cos(y)(1+\sin(y))}{1-\sin^2(y)}[/tex]
[tex]\frac{\cos(y)(1+\sin(y))}{cos^2(y)}[/tex]
In that last step, I apply the Pythagorean Identity I mentioned way above.
Now You have a factor of cos(y) on top and bottom, so you can cancel them out. What we are really saying is that cos(y)/cos(y)=1.
[tex]\frac{1+\sin(y)}{cos(y)}[/tex]
This is the desired result.
We are done.
What are the coordinates of the image of vertex F after a
reflection across the line y=-X?
(-1,-3)
(3,-1)
(1,3)
(-3,1)
G(-2. -3)
F(1.-3)
E -1, -5
H(2-5)
This takes too long to do. I will provide the steps.
For each point given, plug into the equation y = - x.
Point 1:
(-1, -3)
y = -x
y = -(-1)
y = 1
The first point reflected across the line y = - x is (-1, 1).
Do the same with the remaining points.
Find the equation for the linear function that passes through the points (−5,−6) and (10,3). Answers must use whole numbers and/or fractions, not decimals.
A.Use the line tool below to plot the two points_______
B.State the slope between the points as a reduced fraction________
C.State the y-intercept of the linear function_______
D.State the linear function_________
Answer:
Slope: [tex]\frac{3}{5}[/tex]
Y-intercept: -3
Equation: [tex]y=\frac{3}{5} x-3[/tex]
Graph is attached.
Step-by-step explanation:
To find your slope using two points, use the slope formula.
[tex]\frac{y2-y1}{x2-x1} \\[/tex]
Your y1 is -6, your y2 is 3.
Your x1 is -5, your x2 is 10.
[tex]\frac{3-(-6)}{10-(-5)} \\\\\frac{9}{15} \\\\\frac{3}{5} \\[/tex]
Now that you have your slope, use it and one of your points in point-slope form to find your y-intercept.
[tex]y-y1=m(x-x1)\\y-3=\frac{3}{5} (x-10)\\y-3=\frac{3}{5} x-6\\y=\frac{3}{5} x-3[/tex]
Answer:
A. In the graph,
Go 5 units left side from the origin in the x-axis then from that point go downward 6 unit, we will get (-5, -6),
Now, go 10 unit right from the origin in the x-axis then from that point go upward 3 unit, we will get (10, 3),
B. The slope of the line passes through (-5, -6) and (10, 3),
[tex]m=\frac{3-(-6)}{10-(-5)}=\frac{3+6}{10+5}=\frac{9}{15}=\frac{3}{5}[/tex]
C. Since, the equation of a line passes through [tex](x_1, y_1)[/tex] with slope m is,
[tex]y-y_1=m(x-x_1)[/tex]
Thus, the equation of the line is,
[tex]y+6=\frac{3}{5}(x+5)----(1)[/tex]
For y-intercept,
x = 0,
[tex]y+6 = \frac{3}{5}(0+5)\implies y = 3-6=-3[/tex]
That is, y-intercept is -3.
D. From equation (1),
[tex]5y + 30 = 3x + 15[/tex]
[tex]\implies 3x - 5y = 15[/tex]
Which is the required linear function.
Algebra 2 help? will give brainliest
n a concert band, the probability that a member is in the brass section is 0.50. The probability that a member plays trombone, given that he or she is in the brass section, is 0.36. What is the probability that a randomly selected band member is in the brass section and plays trumpet?
A) 0.50
B) 0.72
C)0.14
D)0.18
Answer:
The correct option is D
Step-by-step explanation:
To find the solution of this problem firstly we will find the probability that some one is in the brass section and play trombone.
We will multiply the probability that a member is in the brass section which is 0.50 with the probability that a member plays trombone, given that he or she is in the brass section which is 0.36
= 0.50 * 0.36
=0.18
Therefore the probability that a randomly selected band member is in the brass section and plays trumpet is 0.18
Thus the correct option is D....
Answer:
D
Step-by-step explanation:
What is Y=3/4+2 graphed
Answer:
I don't possess a graph so I'll teach it to you.
Step-by-step explanation:
In a coordinate plane with 4 quadrants, the formula for this equation is SLOPE. This is fairly a very easy topic to learn about. The formula is y = mx + b.
So I assume you forgot to put the "x" after the 3/4.
Anyway, to answer this the "2" in bthe equation is the y-intercept. So the X-coordinate will ALWAYS be ZERO! O basically you plot at (0,2).
Next, you grab the slope. To get it you must use the RISE OVER RUN technique. You rise 3 UP and since it's a POSITIVE SLOPE, 3/4, NOT -3/4, you RUN 4 units to the RIGHT, which gives you (5,4), I believe. And you keep doing that until the graph is finished. And if you want to go backwards from (0,2), you make the RISE AND RUN, NEGATIVE. It's very simple. In the end you should get a line like "/" on your graph which means it's a POSITIVE SLOPE. If it's "\", IT'S A NEGATIVE SLOPE.
I hope this helps and PLEASE FOLLOW ME! I JUST STARTED BRAINLY!
Bethany wrote the equation x+(x+2)+(x+4)=91 when she was told that the sum of three consecutive odd integers had a sum of 91. Which statement about her equation is true?
A) Bethany is correct because consecutive odd integers will each have a difference of two.
B) Bethany is correct because there are three xs in the equation and three is an odd number so it represents the sum of odd numbers.
C) Bethany is incorrect because 2 and 4 are even numbers, she should use 1 and 3 in their place.
D) Bethany is incorrect because consecutive integers always increase by 1 each time, not by 2.
Answer:
Bethany is correct because consecutive odd integers will each have a difference of two.
For example: [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21...] All those are odd numbers, and have a difference of two.
So every time time we make 'x' an odd number in Bethany's equation, we will get three consecutive numbers.
For example, if 'x' equals '1', then we will get the three consecutive numbers 1, 3 and 5.
If 'x' equals 7, then we will get the three consecutive numbers 7, 9 and 11.
Answer:
A.) Bethany is correct because consecutive odd integers will each have a difference of two
Step-by-step explanation:
The sum of 3 consecutive odd integers is 91. Let the first odd integer is x. The next odd integer will be obtained by adding 2 in x i.e. (x + 2). The third odd integer will be obtained by adding 2 in the second odd integer i.e. (x + 2) + 2 = x + 4
After the information stated we can conclude that:
The 3 odd integers will be:
x , (x+2) and (x+4)
Their sum is given to be 91. So we can write:
x + (x+2) + (x+4) = 91
Hence, we can conclude that: Bethany is correct because consecutive odd integers will each have a difference of two.
6x-5y=5
3x+5y=4
The x-coordinate of the solution to this system of equation is
Answer:
x=1
Step-by-step explanation:
1) 6x-5y=5
2) 3x+5y=4
ets perform the following operation
1) +2), This leads to the following equation:
6x+3x-5y+5y=5+4
From where we obtain the solution for x
9x=9
x=1
Which number line represents the solution set for the inequality -4(x+3) ≤ -2 - 2x?
Answer:
d
Step-by-step explanation:
u got the answer right
Can someone help me plz
Step-by-step explanation:
m∠3 + m∠4 = 180°
TRUE - they are supplementary angles
m∠2 + m∠4 + m∠6 = 180°
TRUE - measureas of angles in a triangle add up to 180°
m∠2 + m∠4 = m∠5
TRUE, because
m∠2 + m∠4 + m∠6 = 180° and m∠6 + m∠5 = 180°
therefore m∠2 + m∠4 + m∠6 = m∠6 + m∠5 subtract m∠6 from both sides
m∠2 + m∠4 = m∠5
m∠1 + m∠2 = 90°
FALSE, because m∠1 + m∠2 = 180°
m∠4 + m∠6 = m∠2
FALSE, because
m∠4 + m∠6 + m∠2 = 180° subtract m∠2 from both sides
m∠4 + m∠6 = 180° - m∠2
m∠2 + m∠6 = m∠5
FALSE, because
m∠5 + m∠6 = 180° subtract m∠5 from both sides
m∠6 = 180° - m∠5 add m∠2 to both sides
m∠2 + m∠6 = 180° - m∠5 + m∠2
Factor this trinomial completely.
-6x2 + 26x+ 20
Answer:
−2(3x+2)(x−5)
Step-by-step explanation:
−6x2+26x+20=
=−2(3x+2)(x−5)
Which of the following describe an angle with a vertex at Y?
Check all that apply.
A. XYZ
B. ZXY
C. XZY
D. ZYX
Answer:
A and D
Step-by-step explanation:
See I cannot explain you by diagram as I cannot make it here but the short trick is that the angle with the vertex you are looking for should be in the centre.
Here, it is XYZ and ZYX
Which of the following mixed numberd is represented by the letter A in number line shown?
Answer:
A
Step-by-step explanation:
The line is divided into 9 parts between 1 and 2
A is situated 6 parts of the way between 1 and 2, that is
[tex]\frac{6}{9}[/tex] = [tex]\frac{2}{3}[/tex] ← cancelling by 3
Hence
A = 1 + [tex]\frac{2}{3}[/tex] = 1 [tex]\frac{2}{3}[/tex] → A
I need to be able to take a set of data, and find it's exponential function.
Answer:
The process below should work.
Step-by-step explanation:
Let's pretend we have these two points we are trying to find an exponential equation for: (-2,6) and (2,1).
Exponential equations are of the form [tex]y=a \cdot b^x[/tex] where we must find [tex]a[/tex] and [tex]b[/tex].
So you enter both points into that equation giving you:
[tex]6=a \cdot b^{-2}[/tex]
[tex]1=a \cdot b^{2}[/tex]
I'm going to divide equation 1 by 2 because if I do the a's will cancel and I could solve or b.
[tex]\frac{6}{1}=\frac{a \cdot b^{-2}}{a \cdot b^2}[/tex]
[tex]6=\frac{b^{-2}}{b^2}[/tex]
By law of exponent, I can rewrite the right hand side:
[tex]6=b^{-2-2}[/tex]
[tex]6=b^{-4}[/tex]
Now do ^(-1/4) on both sides to solve for b:
[tex]6^\frac{-1}{4}=b[/tex]
Now we use one of the equations along with our value for b to find a:
[tex]1=a \cdot b^2[/tex] with [tex]b=6^{\frac{-1}{4}}[/tex]
[tex]1=a \cdot (6^{\frac{-1}{4}})^2[/tex]
Simplify using law of exponents:
[tex]1=a \cdot 6^{-\frac{1}{2}}[/tex]
Multiply both sides by 6^(1/2) to solve for a:
[tex]6^{\frac{1}{2}}=a[/tex]
[tex]y=a \cdot b^x[/tex] with [tex]a=6^{\frac{1}{2}} \text{ and } b=6^{\frac{-1}{4}}[/tex] is:
[tex]y=6^\frac{1}{2} \cdot (6^{\frac{-1}{4})^x[/tex]
We can simplify a smidgen:
[tex]y=6^\frac{1}{2} \cdot (6)^\frac{-x}{4}[/tex]
A patrolman spends 25% every day completing paperwork. The patrolmans shift each day is 8 hours. How much of his time does he spend doing paperwork each day
Answer:
2 hours.
Step-by-step explanation:
8 hours x 25 / 100 = 2 hours
Answer:
2 hours.
Step-by-step explanation:
Let the number of hours taken doing paperwork be x.
Shift of each day=8 hours
According to question
x=25%of 8 hours
x=25×8/100
x=2 hours
Thus, answer is 2 hours.
Question 5 (1 point)
Chandler employees 30 people and plans to increase the number of seasonal
workers by 5% each week. Select the correct equation that represents this scenario.
a) Linear: f (x) = 30 + 1.05x
b) Exponential: f (x) = 30(1:05)?
c) Exponential: f (x) = 30(0.05)
d) Linear: f (x) = 30 + 0.05x
Answer:a) Linear: f (x) = 30 + 1.05x
Step-by-step explanation:
Linear: f (x) = 30 + 1.05x is the correct equation.
The answer is option A.
What's an equation example?An equation is a mathematical statement this is made up of expressions related with the aid of the same signal. for instance, 3x – five = 16 is an equation. Solving this equation, we get the price of the variable x as x = 7.
A one-step equation is an algebraic equation you may resolve in the most effective one step. You've got solved the equation when you get the variable through itself, and not using numbers in the front of it, on one side of the same signal.
Learn more about the equation here: https://brainly.com/question/1214333
#SPJ2
Which best describes the transformation that occurs from
the graph of f(x) = x2 to g(x) = (x - 2)2 + 3?
right 2, up 3
left 2, down 3
right 2, down 3
left 2, up 3
Answer:
A. right 2, up 3
Step-by-step explanation:
We are asked to find the transformation that occurs from the graph of [tex]f(x)=x^2[/tex] to [tex]f(x)=(x-2)^2+3[/tex].
Let us recall transformation rules:
[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]
[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]
[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]
[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]
Upon looking at our given functions, we can see that graph of [tex]f(x)=x^2[/tex] is shifted to right by 2 units as 2 is inside parenthesis. The graph is shifted upwards by 3 units as we have positive 3 outside parenthesis.
Therefore, option A is the correct choice.
Wingspans of adult herons have approximate normal distribution with mean 125 cm and standard
deviation 12 cm. What proportion of herons have wingspan of exactly 140 cm?
Answer:
0.1056
Step-by-step explanation:
Given from the question;
Mean=125cm
Standard deviation =12cm
You should find the z* value from mean and standard deviation
The formula to apply is;
z=(wingspan in question - mean)÷standard deviation
[tex]z=\frac{140-125}{12} =\frac{15}{12} =1.25[/tex]
Using the Z score table read the value of proportion that corresponds to 1.25
From the table, the proportion is 0.1056
PLEASE ANSWER FIRST GETS BRAINLIEST
Both equations start with y =
Set both equations equal to each other and solve for x first:
1/3x-4 = -7/3x +4
Add 7/3x to both sides:
8/3x - 4 = 4
Add 4 to each side:
8/3x = 8
Divide both sides by 8/3
x = 3
Now you have the value of x, replace x in the equation to solve for y:
y = 1/3(3) -4 = 1-4 = -3
y = -7/3(3) +4 = -7+4 = -3
y = -3
X = 3 and y = -3
Darrin can skateboard 2 miles against a 4 mph wind in the same amount of time he skateboards 6 miles with a 4 mph wind. Find the speed Darrin skateboards with no wind.
Answer:
Speed = 8mph
Step-by-step explanation:
Speed of wind = 4mph
Let speed of Darrin with no wind be "x" mph
then resultant speed of Darrin, travelling in direction of wind = (x + 4) mph
Using a result, Time = Distance travelled / Net speed
Time taken by Darrin to travel 6miles in direction of wind = 6 / (x + 4)
When Darrin travel in opposite direction of wind, then its net speed = (x - 4)mph
Darrin travel 2 miles against the wind in 6/(x + 4) hr
then Distance = speed × time
2 = ( x- 4 ) × ( 6/x + 4)
2x + 8 = 6x - 24
4x = 32
x = 8 mph
Therefore speed of Darrin skateboard with no wind = 8mph
Answer:
Speed without wind will be 8 mph
Step-by-step explanation:
Now by revising basic formula here
Velocity = Distance/Time. . . . (A)
Assume speed without wind is 'x'
When Darrin is moving against wind to cover 2 miles;
net speed will be x-4
When Darrin is moving along with the wind to cover 6 miles;
net speed will be x+4
Please note that the time for covering distance of 2 miles and 6 miles is same,
So, from equation (A)
Time = Distance/Velocity,
Time for 2 miles will be
Time = 2/(x-4)
Time for 6 miles will be
Time = 6/(x+4)
Since, the time for both distances is same, here we can equate,
2/(x-4) = 6/(x+4)
by cross multiply
2(x+4) = 6(x-4)
2x+8 = 6x-24
4x = 32
x = 8
So, 8 miles per hour is the speed of Darrin if there is no wind.
Select which form to use when you know the slope of the line and one of the points on the line.
a horizontal line
C slope-intercept for
b. vertical line
d. point-slope form
Answer:
d
Step-by-step explanation:
Definitely choose the point-slope form y - k = m(x - h) (Answer d)
Final answer:
To write the equation of a line when you have the slope and a single point on the line, the D) point-slope form is the most suitable formula to use.
Explanation:
When you know the slope of a line and a point on the line, the best form to use is the point-slope form. The point-slope formula is expressed as y - y1 = m(x - x1), where m is the slope and (x1, y1) is the known point. This formula allows you to plug in the slope and the coordinates of the point directly to form the equation of the line.
The slope-intercept form y = mx + b is used when you know the slope and the y-intercept, while the point-slope form is specifically designed to formulate an equation given a point and the slope of the line. A horizontal line, which has a slope of zero, nor a vertical line, which has an undefined slope, would not apply to this particular situation.
Say you have $14,000 to invest into an investment account. You can either invest your money into an account with a 7% annual interest rate which is compounded quarterly, or an account with a 6.8% annual interest rate which is compounded monthly, which should you choose for a 15-year investment?
Answer:
You should choose an account with a 7% annual interest rate which is compounded quarterly
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
part 1)
we have
[tex]t=15\ years\\ P=\$14,000\\ r=0.07\\n=4[/tex]
substitute in the formula above
[tex]A=14,000(1+\frac{0.07}{4})^{4*15}[/tex]
[tex]A=14,000(1.0175)^{60}[/tex]
[tex]A=\$39,645.43[/tex]
part 2)
we have
[tex]t=15\ years\\ P=\$14,000\\ r=0.068\\n=12[/tex]
substitute in the formula above
[tex]A=14,000(1+\frac{0.068}{12})^{12*15}[/tex]
[tex]A=14,000(1.0057)^{180}[/tex]
[tex]A=\$38,713.11[/tex]
What is x^2/3y/x^2/3y^1/3 in exponential form?
Answer: option b
on edg guys:))
Step-by-step explanation:
y ^2/3
Find the measure of HG¯¯¯¯¯¯¯¯.
A. 12
B. 16
C. 14
D. 7
HG^2 = FG * (FG + EF)
Fill in the values:
(x+3)^2 = x * (7+x)
Simplify the right side:
(x+3)^2 = 7x +x^2
Rewrite the left side using the FOIL method
x^2 + 6x + 9 = 7x +x^2
Subtract x^2 from both sides:
6x +9 = 7x
Subtract 6x from both sides:
x = 9
Now you have x solve for HG
HG = x +3 = 9+3 = 12
The answer is A.
(Free points)
Factorise x³ + 216y³ + 8z³ - 36xyz
Answer:
[x+6y+2z][x²+(6y)²+(2z)²-6xy-12yz-2xz]
Step-by-step explanation:
x³+216y³+8z³-36xyz
x³+(6y)³+(2z)³-3×6×2×xyz
As we know
a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)
Let a=x
b=6y
c=2z
Now.
[x+6y+2z][(x²+(6y)²+(2z)²-x×6y-6y×2z-x×2z]
[x+6y+2z][x²+(6y)²+(2z)²-6xy-12yz-2xz]
Answer:
have a good day
Step-by-step explanation:
you deserve it
Multiplying monomials and binomials
Answer:
The product of 28w(w-17) is 28w^2 - 476w
Step-by-step explanation:
Given
28w(w-17)
We have to find the product of the monomial and binomial polynomials
The term 28w will be distributed to w-17
So,
= (28w)(w) - (28w)(17)
= 28w^2 - 476w
Therefore, the product of 28w(w-17) is 28w^2 - 476w ..
Final answer:
When multiplying monomials and binomials, you can follow certain rules. Multiply the numerical coefficients, add the exponents of the variables, and then combine like terms if possible.
Explanation:
When multiplying monomials and binomials, you can follow a few rules. For monomials, you simply multiply the numerical coefficients and add the exponents of the variables. For binomials, you can use the distributive property to multiply each term of one binomial by each term of the other binomial. Then, combine like terms if possible.
For example, let's say we have (2x^2)(3x^3). We would multiply the coefficients (2 * 3 = 6) and add the exponents of the variable x (2 + 3 = 5). So the resulting expression is 6x^5.
Which of the following expressions represents the distance between 5/2 and 4 7/8 on a number line?
Answer:
C. None of the aboveStep-by-step explanation:
[tex]\text{The formula of a distance between x and y on a number line:}\\\\d=|b-a|=|a-b|\\\\\text{We have}\ a=\dfrac{5}{2}\ \text{and}\ b=4\dfrac{7}{8}.\ \text{The distance:}\\\\d=\left|\dfrac{5}{2}-4\dfrac{7}{8}\right|=\left|4\dfrac{7}{8}-\dfrac{5}{2}\right|}[/tex]
Answer:
none of the above
Step-by-step explanation:
What is sin -1 (1/2) if the terminal side of 0 is located in quadrant 1
Answer:
sin^-1 (1/2) = 30°
Step-by-step explanation:
* Lets explain how to find the trigonometry functions from the unit circle
- The unit circle is the circle whose radius is 1 unit
- It intersects the four axes at:
# Positive part of x-axis at (1 , 0) and negative part at (-1 , 0)
# Positive part of y-axis at (0 , 1) and negative part at (0 , -1)
- The terminal of any angle intersect it at point (x , y) where x² + y² = 1
- If The angle between the terminal side and the x-axis is Ф , then
# The adjacent side of Ф = x
# The opposite side of the angle Ф = y
- In the problem the terminal side lies in the first quadrant
∴ all the trigonometry functions are positive
∵ sin Ф = opposite/hypotenuse
∵ The opposite = 1/2 and the hypotenuse is the terminal side = 1
∴ sin Ф = 1/2 ÷ 1 = 1/2
- To find Ф use the inverse function sin^-1 Ф
∵ sin Ф = 1/2
∴ Ф = sin^-1 (1/2)
∴ Ф = 30°
* sin^-1 (1/2) = 30°
If f(x) = 3x? - 4 and g(x) = x+2, find (f - g)(x).
O
O
O
O
A. 3x2 - *-6
B. 3x2 - x-2
C. 3x -8
D. *- 3x - 2
Answer:
The answer is A, (3x2-x-6)
Step-by-step explanation:
f(x)=3x2 -4
g(x)=x+2
f(x)-g(x)= 3x2-4 -x-2= 3x2-x-6
Final answer:
The expression (f - g)(x) is found by subtracting g(x) from f(x) and simplifying, which results in 3x² - x - 6, corresponding to option A.
Explanation:
To find (f - g)(x) when f(x) = 3x² - 4 and g(x) = x + 2, we need to subtract the function g(x) from f(x). The operation looks like this:
(f - g)(x) = f(x) - g(x) = (3x² - 4) - (x + 2)
Let's perform the subtraction step by step:
Distribute the negative sign to both terms in g(x):
(3x²- 4) - x - 2
Combine like terms:
3x² - x - 4 - 2
Final simplification:
3x² - x - 6
Therefore, the correct answer is 3x² - x - 6, which matches option A from the provided choices.